Average return vs CAGR

A friend told me last week his fund had averaged a great year. Up 50 percent, then down 50. So it broke even, he figured.

It did not. Rs 100 goes to 150, then loses half of that, and lands at 75. He is down a quarter. The average of the two years is zero. The money is down 25 percent. Two different numbers, and only one of them pays for anything.

This is the quietest trap in investing. The number a fund advertises is the average return. The number your money actually earns is the CAGR, the rate that compounds. They match only when the path is a straight line, and no fund rides a straight line. Every swing pulls the two apart, and the wilder the swings, the wider the gap.

Here is where it starts costing money. Picture two funds, both averaging 12 percent a year. Identical on the brochure. One swings 8 percent, the other 30. What actually compounds is 11.68 percent against 7.50. Put Rs 10 lakh in each for twenty years and the calm fund lands near Rs 91 lakh while the wild one limps in around Rs 42 lakh. Same average. Half the money.

The drag has a formula. Close to the volatility squared, divided by two. At 8 percent swings it shaves a third of a point a year. At 30 percent it eats four and a half points, taken before you ever see the headline.

Three things I keep coming back to. The brochure shows the average, your account shows the CAGR, and only the second is real. Volatility is a tax, not a vibe. And a smoother 11 beats a wilder 13 over a long enough horizon, which is the whole reason drawdown matters and rebalancing earns its keep.

The average return is the story the fund tells. The geometric return is the receipt your money writes. The gap between them is the volatility tax, and nobody mails you the bill.

Up 50, down 50, drawn out

The friend's two years are the cleanest way to see the gap, so here they are on one picture.

The CAGR is the steady rate that would have got you from Rs 100 to Rs 75 in two years: 0.75 ^ (1 / 2) minus 1 = minus 13.4 percent a year. That is the number that matches the money.

Try any pair of years yourself. The average and the CAGR only agree when both years are the same.

A real example: the bigger average lost

Textbook pairs are easy to dismiss, so I went to our own model lines. I took the month end values at each December and worked out four calendar years, 2022 to 2025, for two of them.

Now do the two calculations for each row.

The Healthcare Basket model averages (minus 19.6 + 57.5 + 40.1 + 0.5) / 4 = 19.6 percent. Multiply the years instead: 0.804 x 1.575 x 1.401 x 1.005 = 1.783. The CAGR is 1.783 ^ (1 / 4) minus 1 = 15.6 percent.

The Nifty 50 Equal Weight model averages 18.2 percent. Its four years multiply to 1.928, a CAGR of 17.8 percent.

The model with the higher average, 19.6 against 18.2, compounded slower, 15.6 against 17.8. One minus 19.6 percent year did most of the damage: everything after it had to rebuild a smaller base. Rs 1,00,000 in each at the end of 2021 would have been about Rs 1.78 lakh and Rs 1.93 lakh four years later.

Four years is a short window, and I would not read anything about the future into these two lines. The point is narrower. Rank by the average and you pick Healthcare. Rank by what the money did and you pick Equal Weight.

Why the brochure prefers the average

The average of yearly returns is always equal to or higher than the CAGR over the same years. They are equal only when every year is identical. So when someone wants a bigger number, the average is the honest looking way to get it. Nothing in it is false. It just answers a question nobody's account asks.

For the twenty year pair in the opening, the receipts are Rs 10,00,000 x 1.1168 ^ 20 = about Rs 91 lakh and Rs 10,00,000 x 1.075 ^ 20 = about Rs 42 lakh. The volatility version of this idea, with the squared rule worked through, is in volatility drag.

The free Learn module on performance measurement covers CAGR, rolling returns and the risk adjusted ratios with quizzes and a certificate.